Ramberg-Schmeiser distribution

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Description

Computes the pdf, cdf, value at risk and expected shortfall for the Ramber-Schmeiser distribution due to Ramberg and Schmeiser (1974) given by

\begin{array}{ll} &\displaystyle {\rm VaR}_p (X) = \frac {p^b - (1 - p)^c}{d}, \\ &\displaystyle {\rm ES}_p (X) = \frac {p^{b}}{d (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p d (c + 1)} \end{array}

for 0 < p < 1, b > 0, the first shape parameter, c > 0, the second shape parameter, and d > 0, the scale parameter.

Usage

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varRS(p, b=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
esRS(p, b=1, c=1, d=1)

Arguments

p

scaler or vector of values at which the value at risk or expected shortfall needs to be computed

d

the value of the scale parameter, must be positive, the default is 1

b

the value of the first shape parameter, must be positive, the default is 1

c

the value of the second shape parameter, must be positive, the default is 1

log

if TRUE then log(pdf) are returned

log.p

if TRUE then log(cdf) are returned and quantiles are computed for exp(p)

lower.tail

if FALSE then 1-cdf are returned and quantiles are computed for 1-p

Value

An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the values at risk or expected shortfall computed at p.

Author(s)

Saralees Nadarajah

References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

Examples

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x=runif(10,min=0,max=1)
varRS(x)
esRS(x)

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